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Given y=ln(1/x)
y'=(1/(1/x))(-x-2)=(1/(1/x))(1/x2)=x/x2=1/x
Use the chain rule. The derivative of ln(x) is 1/x. Instead of just "x" inside the natural log function, it's "1/x". Since the inside of the function is not x, the derivative must be multiplied by the derivative of the inside of the function.
So it's
1/(1/x) [the derivative of the outside function, natural log]
times
-x-2=1/x2 [the derivative of the inside of the function, 1/x]
This all simplifies to 1/x
So the derivative of ln(1/x) is 1/x
What else can I help you with?
What is the derivative of ln 1 divided by 1-x?
0
What is the derivative of 1 divided by x to the third power?
1 divided by x to the third power equals x to the negative third. The derivative of x to the negative third is minus three x to the negative fourth.
What is the derivative of 4 divided by X?
-4/x2
What is the derivative of 1 divided by fx under the conditions that fx is differentiable and fx cannot be 0?
Negative the derivative of f(x), divided by f(x) squared. -f'(x) / f²(x)
What is the derivative of x divided by 3?
The derivative of x divided by 3 is 1/3. This can be found using the power rule of differentiation, where the derivative of x^n is nx^(n-1). In this case, x can be written as x^1, so the derivative is 1(1/3)*x^(1-1) = 1/3.
What is the derivative of x minus y divided by x plus y?
m
What is the derivative of 1 divided by root x?
(1/2(x^-1/2))/x
What is the derivative of cos x sin x divided by cos x sin x?
(cos x sin x) / (cos x sin x) = 1. The derivative of a constant, such as 1, is zero.
What is the derivative of 1 divided by 1 plus x?
2
What is the derivative of x2 plus 6 divided by 2?
Following the correct order of operations: derivative of x^2 + 6/2 = derivative of x^2 +3, which equals 2x
What is the derivative of 5 divided by x?
Well if you have 5/X then you can rewrite this like 5x-1. And the derivative to that is -5x-2 and that can be rewrote to: -(5/x2).
What is the derivative of root 12 divided by x?
d/dx((√12)/x)=-(√12)/x^2
